Answer
The minimum mass of the hero is $199.5~kg$. This scenario seems a bit unreasonable since the hero would need to be a gigantic character.
Work Step by Step
Let's assume that the center of mass of both people together is at the edge of the cliff and let this point be $x = 0$. Then the hero's center of mass is located at $x = -15~cm$. We can find the minimum mass of the hero $m_h$:
$x_{com} = \frac{(m_h)(-15~cm)+(68~kg)(44~cm)}{m_h + 68~kg}$
$0 = \frac{(m_h)(-15~cm)+(68~kg)(44~cm)}{m_h + 68~kg}$
$0 = (m_h)(-15~cm)+(68~kg)(44~cm)$
$(m_h)(15~cm) = (68~kg)(44~cm)$
$m_h = \frac{(68~kg)(44~cm)}{15~cm}$
$m_h = 199.5~kg$
The minimum mass of the hero is $199.5~kg$. This scenario seems a bit unreasonable since the hero would need to be a gigantic character.
